#### Solved Examples and Worksheet for Areas of Triangles

Q1Find the area of a triangle whose base is 5 in. and height is 6 in.
A. 17 in2
B. 19 in2
C. 15 in2
D. 14 in2

Step: 1
Area of a triangle = 12 × base × height
Step: 2
= 12 × 5 × 6
[Substitute base = 5 and height = 6.]
Step: 3
= 302 = 15
[Simplify.]
Step: 4
The area of the triangle is 15 in2.
Correct Answer is :   15 in2
Q2What is the area of the triangle, if the height of the triangle is two times the base and the base length is 9 m?

A. 7 m2
B. 11 m2
C. 81 m2
D. 13 m2

Step: 1
Area of the triangle = 12 × base × height
Step: 2
The height of the triangle is two times the length of the base.
Step: 3
Height of the triangle = 2 × base length = 2 × 9 = 18 m
[Substitute base length = 9.]
Step: 4
Area of the triangle = 12 × 9 × 18
[Substitute the values.]
Step: 5
= 9 × 9 = 81
[Simplify.]
Step: 6
The area of the triangle is 81 m2.
Correct Answer is :   81 m2
Q3Find the area of the triangle whose height is 6 ft and base is three times its height.
A. 59 ft2
B. 108 ft2
C. 49 ft2
D. 54 ft2

Step: 1
The area of the triangle = 12 × base × height
[Formula.]
Step: 2
The base length = 3 × height
= 3 × 6 = 18 ft
[Since base is three times the height.]
Step: 3
So, area of the triangle = 12 × 18 × 6
[Substitute the values.]
Step: 4
= 1082
[Simplify.]
Step: 5
= 54 ft2
[Divide the numerator and the denominator by 2.]
Step: 6
Area of the triangle = 54 ft2.
Correct Answer is :   54 ft2
Q4BC is 6 cm and the height of the triangle ABC is 5 cm. Find the area of the shaded region of the figure, if the area of the triangle DEF is 5 cm2.

A. 13 cm2
B. 10 cm2
C. 12 cm2
D. 11 cm2

Step: 1
Area of the shaded region of the figure = area of the triangle ABC - area of the triangle DEF
Step: 2
Area of a triangle with base b and height h = 12 × b × h
Step: 3
The area of the triangle ABC = 12 × BC × height of the triangle ABC = 12 × 6 × 5.
[Substitute BC = 6 cm and height = 5 cm.]
Step: 4
= 302 = 15 cm2
[Simplify.]
Step: 5
The area of the shaded region of the figure = 15 - 5
[Substitute the areas of the triangles.]
Step: 6
= 10 cm2
[Subtract.]
Step: 7
The area of the shaded region of the figure = 10 cm2.
Correct Answer is :   10 cm2
Q5X, Y and Z are the mid-points of the corresponding sides of the isosceles triangle ABC. What is the area of the shaded region, if AB = 6 m, BC = 8 m, XP = 2 m and the area of the triangle ABC is 16 m2?

A. 33 m2
B. 18 m2
C. 8 m2
D. 16 m2

Step: 1
In the figure, BY = YC = BC2 = 82 = 4 m
[Since Y is the midpoint of BC.]
Step: 2
Area of the parallelogram XBYZ = base x height = BY × XP
Step: 3
= 4 × 2 = 8 m2
[Substitute BY = 4 and XP = 2.]
Step: 4
Area of the shaded region = Area of the triangle ABC - Area of the parallelogram XBYZ
Step: 5
= 16 - 8 = 8 m2
[Substitute and subtract.]
Correct Answer is :   8 m2
Q6What is the height of the triangle, if the base of the triangle is twice the height, and its area is 225 yd2?

A. 15 yd
B. 19 yd
C. 16 yd
D. None of the above

Step: 1
Let h is the height of the triangle.
Step: 2
Given, area of the triangle = 225 yd2
The base = twice the height = 2 × h.
Step: 3
Area of a triangle = 12 × base × height
[Formula.]
Step: 4
225 = 12 × 2 × h × h
[Substitute the values.]
Step: 5
225 = h2
[Simplify.]
Step: 6
225 = h2
[Taking square root on both sides.]
Step: 7
15 = h
Step: 8
The height of the triangle = 15 yd.
Correct Answer is :   15 yd
Q7AB is the diameter of the circle. What is the area of the shaded region in the figure?[π = 3.14.]

A. 58.04 in.2
B. 85 in.2
C. 83.04 in.2
D. None of the above

Step: 1
Base of the triangle = 12 in. and the height of the triangle = 5 in.
[Figure.]
Step: 2
The area of ΔABC = 12 × base × height
[Formula.]
Step: 3
= 12 × 12 × 5
[Substitute the values.]
Step: 4
= 30
[Multiply.]
Step: 5
The area of the triangle ABC = 30 in.2
Step: 6
Area of the circle = π(d2)2
[Formula.]
Step: 7
= 3.14 × (122)2
[Substitute the values.]
Step: 8
= 3.14 × 62

Step: 9
= 113.04
[Simplify.]
Step: 10
The area of the circle = 113.04 in.2
Step: 11
Area of the shaded region = area of the circle - area of the triangle ABC
Step: 12
= 113.04 - 30
[From Steps 5 and 10.]
Step: 13
= 83.04

Step: 14
So, the area of the shaded region is 83.04 in.2
Correct Answer is :   83.04 in.2
Q8What is the area of the triangle ABC in the figure?

A. 4 square units
B. 3 square units
C. 8 square units
D. 6 square units

Step: 1
From the figure, base of the triangle is 2 units, and its height is 3 units.
Step: 2
Area of triangle = 12 × base × height
[Formula.]
Step: 3
Area of the triangle ABC
= 12 × 2 × 3
[Substitute the values.]
Step: 4
= 3 square units

Step: 5
Area of the triangle ABC = 3 square units.
Correct Answer is :   3 square units
Q9Find the area of the triangle, if a = 32 ft, b = 40 ft, and c = 24 ft.

A. 960 ft2
B. 768 ft2
C. 384 ft2
D. 480 ft2

Step: 1
Area of a triangle with base b and height h = 12 × b × h
Step: 2
From the figure, base of the triangle = BC = 32 ft and height of the triangle = AB = 24 ft
Step: 3
Area of the triangle ABC = 12 × 32 ft × 24 ft = 384 ft2
[Substitute the values and simplify.]
Step: 4
The area of the triangle = 384 ft2.
Correct Answer is :   384 ft2
Q10What is the area of the triangle?

A. 820 cm2
B. 360 cm2
C. 184.5 cm2
D. 180 cm2

Step: 1
Base of the triangle is 9 cm and its height is 40 cm.
Step: 2
Area of a triangle = 12 × base × height
Step: 3
= 12 × 9 × 40
Step: 4
= 180
Step: 5
Area of the triangle is 180 cm2.
Correct Answer is :   180 cm2
Q11What is the area of the triangle?

A. 240 cm2
B. 280 cm2
C. 160 cm2
D. 560 cm2

Step: 1
Base of the triangle is 35 cm and height is 16 cm.
Step: 2
Area of a triangle = 12 × base × height
Step: 3
= 12 × 35 × 16
Step: 4
= 280
[Simplify.]
Step: 5
So, area of the triangle is 280 cm2.
Correct Answer is :   280 cm2
• Area